Cover: Topology — A Categorical Approach

MIT Press

Topology — A Categorical Approach

A graduate-level textbook that presents basic topology from the perspective of category theory.

Open access — chapter PDFs Buy from MIT Press YouTube @topology_categorical

English edition cover art by London Tsai.

Chapters

Table of contents · open access

  1. 0. Preliminaries
  2. 1. Examples and Constructions
  3. 2. Connectedness and Compactness
  4. 3. Limits of Sequences and Filters
  5. 4. Categorical Limits and Colimits
  6. 5. Adjunctions and the Compact-Open Topology
  7. 6. Paths, Loops, Cylinders, Suspensions, …

Playlist

Short videos that supplement the material.

  1. What is topology?
  2. The subspace topology
  3. Paths
  4. Compact and Hausdorff
  5. Filters and Ultrafilters (Part I: no topology)
  6. Filters and Ultrafilters (Part II: convergence and topological properties)
  7. Categorical limits and colimits are unique
  8. Compactifications
  9. Exponential Topologies
  10. The Seifert Van Kampen Theorem
  11. Covering Spaces (Part I: intro and based covers)
  12. The category of G-Sets
  13. Covering Spaces (Part II: the big picture)

Reviews